If `A={1,3,5,7)` and `B={2,4,6}`, find `n(BxxA)`

Answer

To find the number of elements in the Cartesian product \( B \times A \), we can follow these steps:

### Step 1: Identify the number of elements in each set
- Set \( A = \{1, 3, 5, 7\} \) has 4 elements.
- Set \( B = \{2, 4, 6\} \) has 3 elements.

### Step 2: Use the formula for the Cartesian product
The number of elements in the Cartesian product \( B \times A \) is given by the formula:
\[ n(B \times A) = n(B) \times n(A) \]
where \( n(B) \) is the number of elements in set \( B \) and \( n(A) \) is the number of elements in set \( A \).

### Step 3: Substitute the values into the formula
- \( n(B) = 3 \)
- \( n(A) = 4 \)

So, we can substitute these values into the formula:
\[ n(B \times A) = 3 \times 4 \]

### Step 4: Calculate the result
\[ n(B \times A) = 12 \]

Thus, the number of elements in \( B \times A \) is 12.

### Final Answer
The number of elements in \( B \times A \) is \( 12 \).

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